Math Problem Statement

solve

What is the measure of angle 3 in the given triangle, where angle 1 is 50° and angle 2 is 70°?

Solution

To solve for the measure of angle 3\angle 3 in the given diagram, let's first analyze the figure step-by-step.

We are given:

  • 1=50\angle 1 = 50^\circ
  • 2=70\angle 2 = 70^\circ
  • The right angle in the triangle, which is 9090^\circ.

Looking at the triangle that includes 1\angle 1, 2\angle 2, and 3\angle 3, we can use the fact that the sum of angles in any triangle is 180180^\circ.

In the small triangle with angles 2\angle 2, 9090^\circ (right angle), and 3\angle 3: Sum of angles=180\text{Sum of angles} = 180^\circ So, 70+90+3=18070^\circ + 90^\circ + \angle 3 = 180^\circ

Now, solve for 3\angle 3: 3=180(70+90)=180160=20\angle 3 = 180^\circ - (70^\circ + 90^\circ) = 180^\circ - 160^\circ = 20^\circ

But, since this is not in the options, let me double-check the interpretation of the angles: Angle 3 must be part of an external angle formed by the large angle at the base with line extensions, as seen in some diagrams, meaning that to find the external measure, you need to subtract from that outside the triangle. I'll

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angle Sum
Exterior Angle

Formulas

Sum of angles in a triangle: angle1 + angle2 + angle3 = 180°

Theorems

Triangle Angle Sum Theorem
Exterior Angle Theorem

Suitable Grade Level

Grades 8-10